# On the structure of the set of coincidence points

## Abstract

We consider the set of coincidence points for two maps between metric spaces. Cardinality, metric and topological properties of the coincidence set are studied. We obtain conditions which guarantee that this set (a) consists of at least two points; (b) consists of at least n points; (c) contains a countable subset; (d) is uncountable. The results are applied to study the structure of the double point set and the fixed point set for multivalued contractions. Bibliography: 12 titles.

- Authors:

- Peoples Friendship University of Russia, Moscow (Russian Federation)
- Voronezh State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22590458

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Sbornik. Mathematics; Journal Volume: 206; Journal Issue: 3; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; HAUSDORFF SPACE; MAPS; METRICS; TOPOLOGY

### Citation Formats

```
Arutyunov, A V, and Gel'man, B D.
```*On the structure of the set of coincidence points*. United States: N. p., 2015.
Web. doi:10.1070/SM2015V206N03ABEH004462.

```
Arutyunov, A V, & Gel'man, B D.
```*On the structure of the set of coincidence points*. United States. doi:10.1070/SM2015V206N03ABEH004462.

```
Arutyunov, A V, and Gel'man, B D. Tue .
"On the structure of the set of coincidence points". United States.
doi:10.1070/SM2015V206N03ABEH004462.
```

```
@article{osti_22590458,
```

title = {On the structure of the set of coincidence points},

author = {Arutyunov, A V and Gel'man, B D},

abstractNote = {We consider the set of coincidence points for two maps between metric spaces. Cardinality, metric and topological properties of the coincidence set are studied. We obtain conditions which guarantee that this set (a) consists of at least two points; (b) consists of at least n points; (c) contains a countable subset; (d) is uncountable. The results are applied to study the structure of the double point set and the fixed point set for multivalued contractions. Bibliography: 12 titles.},

doi = {10.1070/SM2015V206N03ABEH004462},

journal = {Sbornik. Mathematics},

number = 3,

volume = 206,

place = {United States},

year = {Tue Mar 31 00:00:00 EDT 2015},

month = {Tue Mar 31 00:00:00 EDT 2015}

}

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